New results on DNA codes

For q-ary n-sequences, we develop the concept of similarity functions that can be used (for q = 4) to model a thermodynamic similarity on DNA sequences. A similarity function is identified by the length of a longest common subsequence between two q-ary n-sequences. Codes based on similarity functions are called DNA codes. DNA codes are important components in biomolecular computing and other biotechnical applications that employ DNA hybridization assays. We present our unpublished results connected with the conventional deletion similarity function used in the theory of error-correcting codes. The main aim of this paper - to obtain lower bounds on the rate of optimal DNA codes for a biologically motivated similarity function called a similarity of blocks. We also present constructions of suboptimal DNA codes based on the parity-check code detecting one error in the Hamming metric